Islands and continents

I do not whether the short story I am going to tell you fits the requirements of a story about math education, since it takes place in the family. I was about eight-nine years old (Italian third-fourth grade) and I was learning about continents. “Is Australia a continent or an island?” I asked my father. He answered it was BOTH a continent and an island; an answer I found deeply unsatisfactory. I thought for a while about islands and what makes them different from continents, until -weeks later- I reached the conclusion that, by stretching and contracting, Eurasia could be an island of the Oceans as well as an island of the Como lake (“all its shores are on the Como lake”).

A sunny day right after rain I was walking with my mother, I pointed to a puddle and I said: “we are on the island of that puddle”.

She shrugged and replied “why do you always say such stupid things”. (Only many years afterwards I learned that was part of something called topology).